Don’t look now, but Mayor Bill de Blasio is doing something pretty cool: a major infrastructure project to improve New Yorkers’ quality of life, but paid for and run by private companies.

This one’s about improving how New Yorkers and tourists communicate — but the city could apply the same idea to how we get around.

They say you can’t get anything for free, but New York is about to get free Wi-Fi — and real free Wi-Fi.

Starting in July, the city will start replacing its payphones with 7,500 tech kiosks. Once you connect your phone to this new system the first time, your phone will connect to it automatically — meaning that if you’re walking around any crowded part of the city, from Manhattan to major streets in the outer boroughs, you’ll have a strong, fast wireless signal, and without having to watch ads first.

What does this mean? It means real competition for entrenched cellphone companies. If your carrier limits how much data you can use, connecting to free data anytime you are on the streets will help a lot.

It also helps our foreign tourists avoid expensive roaming charges — they can look at maps and do other touristy stuff for free. Plus, each kiosk will have a free tablet, helping the 25 percent of New Yorkers who still don’t have regular access to the Internet.

But the city isn’t paying the $200 million cost of this project itself. Instead, it held a competition, which companies backed by tech giants Google and Qualcomm won. It’s these private firms that will bear the cost and risk of something that is pretty low-tech: getting this thing built.

We think of Wi-Fi as invisible, but this project needs hundreds of miles of new physical cable that goes under our sidewalks and streets. What the private firms get in return: advertising revenue from the kiosks.

But they get something else that they may think is just as valuable: data analysis. The tech companies want to know how people use their phones on the street: what people are looking to do, see or buy when they’re walking around.

We need to do more of this type of thing: competitive infrastructure.

We are, a little. Last week, too, Gov. Andrew Cuomo announced a new way to fix up subway stations.

From now on, contractors competing for this work will be responsible for their cost and schedule overruns — but will have more autonomy, too, to propose what they think will actually work.

But why not apply this idea to a more ambitious project? Real estate developers on the Queens and Brooklyn waterfront want to build a new streetcar line for the people fleeing crowded subways and the even-more-expensive real estate in Manhattan. They’re telling the mayor that the streetcar would cost $1.7 billion, but would bring in more than twice that in new taxes.

If so, though, why wait for the city — which is already strained in paying for its transit projects? The developers should put together their own company to build and run the streetcar — backed only by voluntary assessments on all that waterfront property.

Just like the Wi-Fi folk, the developers would get something in return: more people who want to live and work in their buildings.

Developers could pay the people who run the streetcar a living wage — but not offer them the pensions and health benefits that saddle the rest of our transit system with costs that are so high, we can’t afford to do much else.

Even if streetcar workers unionized — a likely possibility, considering that Citi Bike workers have unionized — negotiators know that even wealthy real estate developers don’t have the deep pockets that the government has. Citi Bike workers get pay and benefits more akin to what workers elsewhere in the private sector get, not, say, nearly free health care for life.

From the city and the state, they’d only need cooperation: space on the streets to move the streetcars past traffic fast, and a deal with the MTA so that people could use their MetroCards.

People may say that’s crazy: That’s not how we do things. But how we do things is crazy: transit projects that come in years late and billions over budget.

Nicole Gelinas is a contributing editor to the Manhattan Institute’s City Journal.